Ministers are set to look again for someone to replace Lord Patten, 70, as chairman of the broadcaster’s governing body.

Olympics chief Lord Coe, 57, who was the Prime Minister’s first choice, decided not to go for the £110,000-a-year position.

“The role has been seen as a “poisoned chalice” after recent BBC troubles”

Martyn Rose, chairman of English National Opera, Sir Peter Bazalgette, 61, chairman of Arts Council England, and Baroness Hogg, 68, a former policy adviser to ex-PM Sir John Major, are among those who have also ruled themselves out.

The role has been seen as a “poisoned chalice” after recent BBC troubles, including the Jimmy Savile scandal.

There was also a £100million failure of an IT project and controversy about huge payoffs to former executives.